A five gallon is not large enough for even a small school of cory cats (4). It is certainly not large enough to support both a small school and a betta. Also cory cats do almost nothing in terms of reducing algae in the tank. I would suggest moving the tank if you don't want algae on the decor.

Corydoras usually don't eat algae...You might want to block the side of the tank that is getting sunlight or move the tank, sometimes when a tank is too close to a window the sun creates algae. I wouldn't add anything but a snail or shrimp in with a betta in a 5 gallon.Amano shrimp will eat some types of algae.